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arXiv · 1409.8475

On the temporal decay of solutions to the two-dimensional nematic liquid crystal flows

Qiao Liu
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Abstract

We consider the temporal decay estimates for weak solutions to the two-dimensional nematic liquid crystal flows, and we show that the energy norm of a global weak solution has non-uniform decay \begin{align*} \|u(t)\|_{L^{2}}+\|\nabla d(t)\|_{L^{2}}\rightarrow 0\quad \text{ as } t\rightarrow \infty, \end{align*} under suitable conditions on the initial data. We also show the exact rate of the decay (uniform decay) of the energy norm of the global weak solution.

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Qiao Liu. 2014-09-30. On the temporal decay of solutions to the two-dimensional nematic liquid crystal flows. https://arxiv.org/abs/1409.8475

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